Vector has a magnitude of $13\mathrm{.}8$ units and points due west. Vector points due north. $($a$)$ What is the magnitude of if $+$ has a magnitude of $16\mathrm{.}8$ units? $($b$)$ What is the direction of $+$ relative to due west? $($c$)$ what is the magnitude of if $-$ has a magnitude of $16\mathrm{.}8$ units? $($d$)$ What is the direction of $-$ relative to due west?

$($Note: Use the convention that an angle north of west is positive, and an angle south of west is negative.$)$